Not talking about archaelogical finds or similar, talking about what part of their culture of society we can see in our current western society if there's any?
Apparently the fasces comes from Etruscan culture. This is the Roman symbol of a magistrate's power, consisting of a double-headed axe in a bundle of wooden rods. While the physical item is no longer used as far as I know, the symbols is still widely used. The Italian Fascists used the symbol, but so do several other current legal systems. I gather it is shown behind the podium of the US House of Representatives.
One trivial thing: the Latin miles ("soldier") is thought to come from Estruscan - and hence to the modern English "military".